This paper presents the extension of the Kutta-Joukowski theorem to unsteady linear aerodynamics. Starting from the formulation developed by Theodorsen for the solution of the velocity potential for circulatory flows around thin, rectilinear airfoils, the frequency response function between bound circulation and circulatory lift is derived. To provide a formulation suitable for time-domain applications, two finite-state approximations of the Kutta-Joukowski frequency response function, with different degrees of complexity and accuracy, are also proposed. The validity of the derived unsteady Kutta-Joukowski theorem is verified by correlation with numerical predictions of the circulatory lift given by a validated boundary-elementmethod solver for potential flows. Furthermore, the proposed finite-state approximations of the unsteady Kutta-Joukowski theorem are applied to problems concerning the circulatory lift response to damped oscillatory airfoil motion and gust perturbation. The higher-accuracy finite-state model provides predictions that correspond perfectly to those obtained by the con-